August 22, 2006

Dwave superconducting quantum continued

The way the AQC model works is that you build an array of qubits (say a square grid for example) with programmable couplers between qubits (see here for some published info on one of D-Wave’s programmable couplers). The settings of these couplers, together with individual biases (favoring one qubit state over the other) on each qubit, comprise the machine language of an AQC. The user of the AQC (1) starts the machine with all of the couplers turned off and all of the local biases favoring the 0 qubit state; (2) turns on a tunneling term between the qubit states of each qubit; (3) slowly turns off the tunneling term while tuning the couplers and local biases to their target values; (4) measures the final states of the qubits.

Adiabatic quantum computation is a novel paradigm for the design of quantum algorithms — it is truly quantum in the sense that it can be used to speed up searching by a quadratic factor over any classical algorithm. On the question of whether this new paradigm may be used to efficiently solve NP-complete problems on a quantum computer — we showed that the usual query complexity arguments cannot be used to rule out a polynomial time solution. On the other hand, we argue that the adiabatic approach may be thought of as a kind of ‘quantumlocal search’. We designed a family of minimization problems that is hard for such local search heuristics, and established an exponential lower bound for the adiabatic algorithmfor these problems. This provides insights into the limitations of this approach. In an upcoming paper [5], we generalize these techniques to show a similar exponential slowdown for 3SAT. It remains an open question whether adiabatic quantum computation can establish an exponential speed-up over traditional computing or if there exists a classical algorithm that can simulate the quantum adiabatic process efficiently.

From the first paper on scaling superconducting AQC:the maximum number of qubits at operating temperature T is {function} ... the energy gap of the problem Hamiltonian .... max number of qubits using advanced josephson junctions and higher temperature superconductors could be hundreds or thousands.